Victor Gershevich (Grigorievich) Kac (; born 19 December 1943) is a Soviet and American mathematician at MIT, known for his work in

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

. He co-discovered Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the

Virasoro algebra In mathematics, the Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string theory. It is named after Miguel Ángel ...

. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler.

Biography

Kac studied mathematics at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

, receiving his MS in 1965 and his PhD in 1968. From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Machine Building (MIEM). He left the

Soviet Union The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship and the Medal of the Collège de France, both in 1981, and a

Guggenheim Fellowship Guggenheim Fellowships are Grant (money), grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon Guggenheim, Simon and Olga Hirsh Guggenheim. These awards are bestowed upon indiv ...

in 1986. He received the

Wigner Medal The International Colloquium on Group Theoretical Methods in Physics (ICGTMP) is an academic conference devoted to applications of group theory to physics. It was founded in 1972 by Henri Bacry and Aloysio Janner. It hosts a colloquium every tw ...

(1996) "in recognition of work on affine

Lie algebras In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identi ...

that has had wide influence in

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

". In 1978 he was an invited speaker (''Highest weight representations of infinite dimensional Lie algebras'') at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

(ICM) in

Helsinki Helsinki () is the Capital city, capital and most populous List of cities and towns in Finland, city in Finland. It is on the shore of the Gulf of Finland and is the seat of southern Finland's Uusimaa region. About people live in the municipali ...

. Kac was a plenary speaker at the 1988

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

centennial conference. In 2002 he gave a plenary lecture, ''Classification of Supersymmetries'', at the ICM in Beijing. Kac is a Fellow of the

, an honorary member of the Moscow Mathematical Society, Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

and a Member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

. The research of Victor Kac primarily concerns

and

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

. His work appears in mathematics and physics and in the development of

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

and the theory of integrable systems. Kac has published 13 books and over 200 articles in mathematics and physics journals and is listed as an ISI highly cited researcher. Victor Kac was awarded the 2015 AMS Leroy P. Steele Prize for Lifetime Achievement. He was married with Michèle Vergne and they have a daughter, Marianne Kac-Vergne, who is a professor of American civilization at the university of Picardie. His brother Boris Katz is a principal research scientist at MIT.

Kac–Moody algebra

"Almost simultaneously in 1967, Victor Kac in the USSR and Robert Moody in Canada developed what was to become Kac–Moody algebra. Kac and Moody noticed that if

Wilhelm Killing Wilhelm Karl Joseph Killing (10 May 1847 – 11 February 1923) was a German mathematician who made important contributions to the theories of Lie algebras, Lie groups, and non-Euclidean geometry. Life Killing studied at the University of M ...

's conditions were relaxed, it was still possible to associate to the Cartan matrix a Lie algebra which, necessarily, would be infinite dimensional." – A.J. ColemanColeman, A. John, "The Greatest Mathematical Paper of All Time",
The Mathematical Intelligencer
'' vol. 11, no. 3, pp. 29–38.

Bibliography

* * * * * * *

References

External links

* *Victor Kac, A Biographical Interview

{{DEFAULTSORT:Kac, Victor 1943 births Living people People from Buguruslan 20th-century American mathematicians Russian mathematicians Soviet mathematicians Fellows of the American Academy of Arts and Sciences American people of Russian-Jewish descent Fellows of the American Mathematical Society Moscow State University alumni 21st-century American mathematicians